Can a refrigerator that is 21.5 cubic feet fit in a space that is 21 cubic feet? (1 point)
No, the refrigerator is too big for the space.
To find the volume of the table, we need to split it into simpler figures. Here, the composite figure consists of two rectangular prisms and a rectangular pyramid.
The first rectangular prism has dimensions 12 inches by 12 inches by 4 inches. Its volume is:
Volume of the first prism = 12 in × 12 in × 4 in = 576 cubic inches
The second rectangular prism has dimensions 8 inches by 8 inches by 25 inches. Its volume is:
Volume of the second prism = 8 in × 8 in × 25 in = 1600 cubic inches
The pyramid has a rectangular base with dimensions 30 inches by 2 inches and a height of 30 inches. Its volume is:
Volume of the pyramid = (1/3) × base area × height
= (1/3) × (30 in × 2 in) × 30 in
= 600 cubic inches
To find the total volume of the table, we add the volumes of the two rectangular prisms and the pyramid:
Total volume = 576 cubic inches + 1600 cubic inches + 600 cubic inches
= 2776 cubic inches
Therefore, the volume of the table is 2776 cubic inches.
What is the volume of a cube with a side length of 1.5 in.?
The volume of a cube with a side length of 1.5 in. can be found by calculating 1.5 x 1.5 x 1.5, which equals 3.375 cubic inches. So the volume of the cube is 3.375 cubic inches.
If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2, what is the height of this prism?(1 point)
Let's call the length of the rectangular prism "l", the width "w", and the height "h". We know from the problem that:
- The volume (V) of the rectangular prism is 1.5 cubic inches: V = 1.5 in^3.
We also know that the length and width have a product of 1.5 square inches:
- lw = 1.5 in^2.
We can use these two equations to solve for the height (h):
- Since V = lwh, we can rearrange this to solve for h: h = V/(lw).
- Substituting the given values, we get h = (1.5 in^3) / (1.5 in^2) = 1 in.
Therefore, the height of the rectangular prism is 1 inch.
Lloyd bought a refrigerator that measures 76 cm×76 cm×170 cm to fit in a space with a volume of 975,000 cm3. Will the refrigerator fit in the space? Explain.
To determine if the refrigerator will fit in the space with a volume of 975,000 cm3, we need to compare the volume of the refrigerator to the volume of the space.
The volume of the refrigerator is:
76 cm x 76 cm x 170 cm = 1,169,280 cm3
The volume of the space is:
975,000 cm3
Since the volume of the refrigerator is larger than the volume of the space, the refrigerator will not fit in the space. The space is too small to accommodate the refrigerator.
what is the volume of the rectangular pyramid with a height of 5 mi, base width of 7.5 mi and base length of 7 mi
The formula for the volume of a rectangular pyramid is:
V = (lwh)/3
where:
l = base length
w = base width
h = height
Plugging in the given values, we get:
V = (7 mi x 7.5 mi x 5 mi)/3
V = 262.5 cubic miles
Therefore, the volume of the rectangular pyramid is 262.5 cubic miles.
A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?
The formula for the volume of a rectangular pyramid is:
V = (lwh)/3
where:
l = base length
w = base width
h = height
In this problem, we are given that the base width is 4 cm, the base length is 9 cm, and the height is 21 cm. Plugging in these values, we get:
V = (4 cm x 9 cm x 21 cm)/3
V = 252 cubic cm
Therefore, the volume of the piece of cheese is 252 cubic cm.
A rectangular prism has a volume of 27 in.3. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
The formula for the volume of a rectangular prism is:
V(prism) = lwh
where:
l = length
w = width
h = height
In this problem, we are given that the volume of the rectangular prism is 27 in^3. Let's assume that the base and height of the rectangular pyramid are congruent to the prism, so the length, width, and height of the pyramid are equal. Let's call this value "x". Then, the base area of the rectangular pyramid is x^2.
The formula for the volume of a rectangular pyramid is:
V(pyramid) = (lwh)/3
Since we're assuming the base and height of the pyramid are congruent to the prism, we have:
l = x
w = x
h = x
The volume of the pyramid can now be found using the formula:
V(pyramid) = [(x^2)(x)]/3
V(pyramid) = (x^3)/3
We also know that the volume of the rectangular prism is 27 in^3, so:
27 = x^3
Solving for x, we get:
x = 3
Therefore, the volume of the rectangular pyramid is:
V(pyramid) = (3^3)/3 = 9 in^3
So the volume of the pyramid is 9 cubic inches.
A rectangular pyramid has a volume of 480 in.3. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
The volume of a rectangular pyramid is given by the formula:
V(pyramid) = (lwh)/3
where l, w, and h are the dimensions of the rectangular pyramid. In this problem, we are given that the volume of the rectangular pyramid is 480 in^3.
The volume of a rectangular prism is given by the formula:
V(prism) = lwh
where l, w, and h are the dimensions of the rectangular prism. We know that the base and height of the rectangular prism are congruent to the base and height of the rectangular pyramid. Let's call this dimension "x".
Using this, we can write:
l = x
w = x
h = kx
where k is some constant. Since the base of the pyramid and prism are congruent, we can write:
V(pyramid) = V(prism)
Therefore:
(lwh)/3 = lwh
Multiplying both sides by 3 and simplifying, we get:
wh = 3h
Substituting for l, w, and h in terms of x, we get:
x^2(kx) = 3(kx)
Solving for k, we get:
k = 3/x
Substituting k in terms of x, we get:
V(prism) = lwh
V(prism) = x^2(kx) = x^2(3/x)(x) = 3x^2
We now have an expression for V(prism) in terms of x. To find the value of x, we can use the fact that the volume of the pyramid is 480 in^3:
(lwh)/3 = 480
Substituting for l, w, and h in terms of x, we get:
(x^3k)/3 = 480
Substituting k in terms of x, we get:
(x^3)(3/x)/3 = 480
Simplifying, we get:
x^2 = 160
Taking the positive square root of both sides, we get:
x = 4√10
Substituting x in terms of k, we get:
k = 3/x = 3/(4√10)
Substituting k in the expression for V(prism), we get:
V(prism) = 3x^2 = 3(4√10)^2 = 480
Therefore, the volume of the rectangular prism is 480 in^3.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft.3, what is the volume of the pyramid?
Since the prism and pyramid have the same height and triangular base, the only difference is that the prism has two congruent triangles whereas the pyramid has one.
Let's call the area of the triangle base A and the height h. Then, the volume of the prism is given by:
V(prism) = Ah
We don't know the area or height of the triangle, but since the prism has a volume of 600 ft^3, we can write:
Ah = 600
Now, let's look at the pyramid. The volume of a pyramid is given by:
V(pyramid) = (Ah)/3
where A is still the area of the triangle base and h is the height of the pyramid. We know that the prism and pyramid have the same height, so h is the same for both shapes. We can substitute the expression for Ah from the prism into the formula for the volume of the pyramid:
V(pyramid) = (Ah)/3 = (600)/3 = 200
Therefore, the volume of the pyramid is 200 ft^3.
What is the volume of the composite figure?
To find the volume of the composite figure, we need to separate it into two simpler figures: a rectangular prism and a triangular prism.
Let's start with the rectangular prism, which has a length of 6 cm, a width of 5 cm, and a height of 3 cm. The volume of the rectangular prism is:
V = lwh = (6 cm)(5 cm)(3 cm) = 90 cm^3
Now let's add the triangular prism, which has a triangular base with a height of 3 cm and a base of 5 cm. The length of the triangular prism is the same as the length of the rectangular prism, which is 6 cm. The volume of the triangular prism is:
V = (1/2)Bh x l = (1/2)(5 cm)(3 cm) x (6 cm) = 45 cm^3
To find the volume of the composite figure, we add the volumes of the rectangular and triangular prisms:
V(composite) = V(rectangular prism) + V(triangular prism) = 90 cm^3 + 45 cm^3 = 135 cm^3
Therefore, the volume of the composite figure is 135 cubic centimeters (cm^3).
what is the volume of the composite figure? the numbers are 7 in, 7 in, 7 in, 10 in, 8 in, 16 in
To find the volume of the composite figure, we need to split it into simpler figures. Here, the composite figure consists of two rectangular prisms.
First, we need to find the dimensions of the two rectangular prisms. One prism has dimensions 7 inches by 7 inches by 10 inches and the other has dimensions 8 inches by 7 inches by 16 inches.
Now, we can find the volume of each prism:
Volume of the first prism = 7 in × 7 in × 10 in = 490 cubic inches
Volume of the second prism = 8 in × 7 in × 16 in = 896 cubic inches
To find the total volume of the composite figure, we add the volumes of the two rectangular prisms:
Total volume = 490 cubic inches + 896 cubic inches = 1386 cubic inches
Therefore, the volume of the composite figure is 1386 cubic inches.
what is the volume of the table? the numbers are 12 in, 12 in, 4 in, 8 in, 8 in, 25 in, 30 in, 2 in, 30 in
what is the volume of the movie theater? the numbers are 15m, 15m, 15m, 44m, 20m, 15m, 15m, 15m, 15m, 44m, 15m
To find the volume of the movie theater, we need to break it down into simpler figures. Here, the composite figure can be split into two rectangular prisms.
One rectangular prism has dimensions 15m × 15m × 44m and the other has dimensions 20m × 15m × 44m.
The volume of the first rectangular prism is:
V = l × w × h = 15m × 15m × 44m = 9900 cubic meters
The volume of the second rectangular prism is:
V = l × w × h = 20m × 15m × 44m = 13200 cubic meters
Therefore, the total volume of the movie theater is:
V = 9900 cubic meters + 13200 cubic meters = 23100 cubic meters
Therefore, the volume of the movie theater is 23100 cubic meters.
Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.
The formula for the volume of a rectangular pyramid is:
V = (lwh)/3
where l is the length, w is the width, and h is the height of the pyramid. We are given that the base has an area of 200 square meters and the height of the pyramid is 75 meters.
We are not given the length or width of the pyramid, but we do know that the base is a rectangle, so we can assume that the length and width are both positive values. Let's call the length "l" and the width "w".
We know that the area of the base is 200 square meters, so:
lw = 200
We can solve for one of the variables in terms of the other:
l = 200/w
Now we can substitute this expression for "l" into the formula for the volume of the pyramid:
V = (lwh)/3 = [(200/w)(w)(75)]/3 = 5000/w cubic meters
Therefore, the volume of the rectangular pyramid is 5000/w cubic meters.
We can find the value of "w" by using the fact that the length and width of the base must be positive and the area of the base is 200 square meters. One possible value for "w" is 10, in which case "l" would be 20. Another possible value for "w" is 20, in which case "l" would be 10. Either way, substituting the value of "w" into the formula for the volume of the pyramid gives us:
V = 5000/w = 500 cubic meters
Therefore, the volume of the rectangular pyramid is 500 cubic meters.
could you explain how you got 5000
Yes, of course! To calculate the volume of the rectangular pyramid, we use the formula:
V = (lwh)/3
where:
l is the length of the base
w is the width of the base
h is the height of the pyramid
We are given that the base of the pyramid has an area of 200 square meters, so we can write:
lw = 200
Since the base is a rectangle, we can assume that both the length and width of the base are positive values. Let's call the length "l" and the width "w".
We also know that the height of the pyramid is 75 meters. Substituting these values into the formula for the volume of the pyramid:
V = (lwh)/3
V = (lw × 75)/3
We can substitute the expression we found for "l" in terms of "w" into this equation:
V = [(200/w) × w × 75]/3
Simplifying this expression gives us:
V = 5000/w
So the formula for the volume of the pyramid is V = 5000/w cubic meters.
Now, we need to find the value of "w" that corresponds to a positive length and a positive width of the base. Since we know that the area of the base is 200 square meters, we can solve for "w" using the equation:
lw = 200
If we choose "w" to be 10, then we get:
l × 10 = 200
l = 20
Since "l" and "w" are both positive, this means that we can use "w" = 10 and "l" = 20 to calculate the volume of the rectangular pyramid:
V = 5000/10 = 500 cubic meters
Therefore, the volume of the rectangular pyramid is 500 cubic meters.
Tiffany has white and black shoes in her shoe box. The probability of her pulling out a white pair of shoes is 25. What is the chance of Tiffany randomly pulling out a black pair of shoes?(1 point)
The probability of pulling out a black pair of shoes can be found using the fact that the sum of the probabilities of all possible outcomes is equal to 1.
If the probability of pulling out a white pair of shoes is 25%, then the probability of pulling out a black pair of shoes must be:
P(black shoes) = 1 - P(white shoes)
= 1 - 0.25
= 0.75
Therefore, the chance of Tiffany randomly pulling out a black pair of shoes is 75% (or 0.75 probability).
In his class, Dale conducted a survey to observe the distribution of eye color. The results are summarized as follows:
Eye Color Number of Students
blue 20
brown 12
green 10
amber 8
hazel 6
gray 4
If a student is randomly chosen from this group, what is the chance of selecting a student with blue eyes? Write your answer in the simplest form of a fraction.
In his class, Dale conducted a survey to observe the distribution of eye color. The results are summarized as follows:
Eye Color Number of Students
blue 20
brown 12
green 10
amber 8
hazel 6
gray 4
If a student is randomly chosen from this group, what is the chance of selecting a student with blue eyes? Write your answer in the simplest form of a fraction.